Problem: Rewrite as a simplified fraction. ${0.80\overline{8} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 808.8888...\\ 100x &= 80.8888...\end{align*}}$ Subtracting the two equations, we have: ${900x = 728}$ ${x = \dfrac{728}{900}} $ ${x = \dfrac{182}{225}} $